# AP Physics C: Mechanics : Interpreting Linear Motion Diagrams

## Example Questions

### Example Question #1 : Interpreting Linear Motion Diagrams

A guillotine blade weighing  is accelerated upward into position at a rate of  .

What is the the approximate mass of the guillotine blade?

Explanation:

The force of gravity on the blade is , which is the same as

This unit relationship comes from Newton's second law.

is the mathematical expression of Newton's second law. The units for force must be a product of the units for mass and the units for acceleration.

Solve the expression by plugging in known values.

### Example Question #1 : Interpreting Linear Motion Diagrams

A guillotine blade weighing  is accelerated upward into position at a rate of  .

What is the tension on the rope pulling the blade, while it is accelerating into position?

Explanation:

The tension in the rope is the sum of the forces acting on it. If one considers that the net force on an object must equal the mass of the object times the acceleration of the object, the net force on the object must be the force due to tension from the rope minus the force due to gravity.

Rearrange the equation.

Plug in known values.

### Example Question #1 : Interpreting Linear Motion Diagrams

Two objects moving in one dimension created the following velocity vs. time graph:

From the graph above, what is true about the two objects at time ?

They are both at rest (not moving)

They are at the same position

They are moving at the same speed

One object is passing the other

They have travelled the same distance from their starting positions

They are moving at the same speed

Explanation:

Since this is a graph of velocity and not position, the curves intersect where the velocities match. Since we do not know the starting position, we do not know where the objects are relative to one another.

### Example Question #2 : Interpreting Linear Motion Diagrams

Two objects moving in one dimension created the following velocity vs. time graph:

From the graph above, which object has traveled a greater distance from its starting position when ?

None of these

Object 1

It cannot be determined from the graph

They have travelled an equal distance

Object 2

Object 1

Explanation:

Since this is a graph of velocity vs. time, its integral is distance travelled. We can estimate the integral by looking at the area under the curves. Since Bbject 1 has a greater area under its velocity curve, it has covered a greater distance. Its velocity is greater that Object 2's for the entire time, so it makes sense that it will travel farther.

### Example Question #21 : Motion

An object is moving in two dimensions. Its vertical motion relative to the horizontal motion is described by the equation . Its motion in the horizontal direction is described by the equation . What is the object's velocity is the  direction in terms of its horizontal position ?

Explanation:

The y velocity is the time derivative of the  position, and not the  derivative. In order to find it, use the chain rule:

Of course,

### Example Question #1 : Interpreting Linear Motion Diagrams

Atwood's machine consists of two blocks connected by a string connected over a
pulley as shown. What is the acceleration of the blocks if their masses are  and .

Assume the pulley has negligible mass and friction.